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Norma-Jean [14]
2 years ago
5

Please help with math question

Mathematics
1 answer:
ELEN [110]2 years ago
7 0

Answer:

y = 4x² -3x +5

Step-by-step explanation:

It can be helpful to plot the points on a graph. The curve through them opens upward, so you know <em>the first two answer choices are incorrect</em>.

<em>Looking at the location of the vertex</em>

The points (-1, 12) and (2, 15) have nearly the same y-value, so the vertex of the parabola will be nearly halfway between those points, at about ...

... x = (-1 +2)/2 = 1/2

Because the point at (2, 15) has a slightly higher y-value, you know it is farther from the vertex, so the vertex will be at an x-value that is less than 1/2.

For quadratic ...

... y = ax² +bx +c

the vertex is found at

... x = -b/(2a)

For the 3rd choice, this is x = -(-4)/(2·3) = 2/3. This is higher than 1/2, so we can eliminate this choice, too.

Only the 4th choice remains. (It passes the vertex location test: x = -(-3)/(2·4) = 3/8 < 1/2.)

_____

There are some other ways to solve this problem, too.

  1. try the given points in the given equations. The +5 as a constant of all of them tell you that all will work for x=0. Both of choices 3 and 4 work for x=-1, so we have to try x=2. Choice 3: 3·2² -4·2 +5 = 9, not 15. Choice 4: 4·2² -3·2 +5 = 15. So Choice 4 is the answer.
  2. write equations for a, b and solve them. a(-1)² +b(-1) +5=12; a(2)² +b(2)+5=15. or a-b=7, 2a+b=5 in standard form. Adding these gives 3a=12, so a=4 and Choice 4 is the answer.
  3. use a graphing calculator to write the quadratic regression formula from the three points. This result is shown in the attachment. The (a, b, c) = (4, -3, 5) correspond to Choice 4.

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liq [111]

Answer:

12πx⁴, 15x⁷, 16x⁹

Step-by-step explanation:

Volume of a cylinder: πr²h

Volume of a rectangular prism: whl

Plugging in variables for the volume of a cylinder, we get: 3x²·(2x)²·π

3x²·(2x)² = 3·2·2·x·x·x·x

= 12·x⁴

=12x⁴

Now, we just multiply that by π.

12x⁴·π = 12x⁴π

A monomial is a 1-term polynomial, so 12x⁴π is a monomial.

Plugging in variables for the volume of a rectangular prism, we get: 5x³·3x²·x²

5x³·3x² = 5·3·x·x·x·x·x

= 15·x⁵

= 15x⁵

Now, we just multiply that by x².

15x⁵·x²

= 15·x·x·x·x·x·x·x

= 15·x⁷

=15x⁷

A monomial is a 1-term polynomial, so 15x⁷ is a monomial.

Same steps for the last shape, another rectangular prism:

2x²·2x³·4x⁴

2x²·2x³

= 2·2·x·x·x·x·x

= 4·x⁵

= 4x⁵

Now, we just multiply that by 4x⁴.

4x⁵·4x⁴

= 4·4·x·x·x·x·x·x·x·x·x·

= 16·x⁹

= 16x⁹

A monomial is a 1-term polynomial, so 16x⁹ is a monomial.

6 0
2 years ago
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lara31 [8.8K]

Answer:

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3 years ago
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Answer: Yes She is correct

Step-by-step explanation:

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Simplify 3^-3<br> Show work
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3 years ago
Solve 15 ≥ -3x or 2/5 x ≥ -2.
ipn [44]

Answer:

x ≥ -5

Step-by-step explanation:

15≥-3x

<em>switch sides</em>

<em>-3x≤15</em>

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<em>(-3x)(-1)≥15(-1)</em>

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